be the successive minima for the convex symmetric set \(B_X\)  and the integer lattice \(\mathbb {Z}^L\) . By Minkowski's theorem
on successive minima (see [1]}) we have
\(\frac{2^L}{L!} \le \operatorname{\mathrm {V}ol}_L\bigl (B_X\bigr ) \lambda _1 \lambda _2 \cdots \lambda _L \le 2^L.\) 
